新生主要参考hduacm版特殊数.pptx

ACM程序设计杭州电子科技大学刘春英

2024/7/192每周一星（10）：wonder618

2024/7/193第十一讲特殊的数

（SpecialNumber）

2024/7/194FibonacciNumberTheseriesbeginswith0and1.Afterthat,usethesimplerule:Addthelasttwonumberstogetthenext.0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,...LeonardoFibonacci1175-1250

2024/7/195KeyWords:1225;Pisa;FibonacciFrederickII;MathCompetition.Wherethiscamefrom?

2024/7/196January

2024/7/197February

2024/7/198March

2024/7/199April

2024/7/1910May、June…???

2024/7/1911Thenumberseriesis——1、1、2、3、5…Thisisfibonaccinumber！Someotherpictures

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2024/7/1916FibonacciGoldenSection

2024/7/1917Fibonacciplants

2024/7/1918Fibonacciplants

2024/7/1919Fibonacciplants

2024/7/1920Fibonacciplants

2024/7/1921sunflowers（向日葵）

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2024/7/1925Catalannumber

2024/7/1926HDOJ_1134:GameofConnections2024/7/1927 Catalannumbers(1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845,...)CatalanNumber(1814—1894Belgium)

2024/7/1928Catalan数有哪些应用?

2024/7/19291.多边形的三角剖分数目4sides,2ways

2024/7/19305sides,5ways

2024/7/19316sides,14ways

2024/7/19327sides,42ways:

2024/7/19332.加括号的方式数目3numbers:(1(23))((12)3)4numbers:(1(2(34)))(1((23)4))((12)(34))((1(23))4)(((12)3)4)

2024/7/1934(1(2(3(45)))) (1(2((34)5)))(1((23)(45))) (1((2(34))5))(1(((23)4)5)) ((12)(3(45)))((12)((34)5)) ((1(23))(45))((1(2(34)))5) ((1((23)4))5)(((12)3)(45)) (((12)(34))5)(((1(23))4)5) ((((12)3)4)5)

2024/7/19353.thenumberofrooted,trivalenttreeswithn+1nodes3nodes:

2024/7/19365nodes:4nodes:

2024/7/19374.thenumberofpathsoflength2nthroughann-by-ngridthatdonotriseabovethemaindiagonal2x2grid:

2024/7/19383x3grid:4x4grid:

2024/7/19395.不同形态二叉树的数目Thereare5binarytreeswith3nodes.

2024/7/19406.其它应用（1）